A theatre company allows a group of 10 people to buy theatre tickets at a price of $28 per person. For each person in excess of 10, the price is decreased by $2 per person for everyone down to a minimum of $10 per person. What number of people will produce the maximum revenue for the theatre company???
Please help. I don't really know how to write out the quadratic equation for this equation. I tried to do revenue=(price)(quantity), but I can't get the right equation at all.
PLEASE HELP PLEASE HELP ME.
To solve this problem, we need to find the number of people that will produce the maximum revenue for the theatre company. To do this, we can use the formula for revenue: Revenue = (Price per person) x (Number of people). However, since the price changes depending on the number of people, we need to express the price as a function of the number of people.
Let's break down the problem step by step:
1. Determine the price per person:
- For the first 10 people, the price is $28 per person.
- For each person in excess of 10, the price decreases by $2 per person, until it reaches a minimum of $10 per person.
2. Express the price per person as a function of the number of people:
- For the first 10 people, the price is constant at $28.
- For each person beyond 10, the price decreases by $2 per person.
- To express this mathematically, we can use a piecewise function:
- For n people, where n > 10, the price per person equals: Price = $28 - ($2 x (n - 10)).
- However, if the price calculated above is less than $10, we need to set the price to $10 instead: Price = Max($10, $28 - ($2 x (n - 10))).
3. Calculate the revenue as a function of the number of people:
- The revenue equals the price per person multiplied by the number of people:
Revenue = Price x Quantity = Price x n.
Now that we have the revenue equation, we can proceed to find the number of people that will produce the maximum revenue for the theatre company. We can do this by finding the value of n that maximizes the revenue function.
If you require further assistance, please provide any additional information or specific values.